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Inference of protein structure from experimental data is of crucial interest in science, medicine and biotechnology. Low-resolution methods, such as small angle X-ray scattering (SAXS), play a major role in investigating important biological questions regarding the structure of proteins in solution. To infer protein structure from SAXS data, it is necessary to calculate the expected experimental observations given a protein structure, by making use of a so-called forward model. This calculation needs to be performed many times during a conformational search. Therefore, computational efficiency directly determines the complexity of the systems that can be explored. We present an efficient implementation of the forward model for SAXS with full hardware utilization of Graphics Processor Units (GPUs). The proposed algorithm is orders of magnitude faster than an efficient CPU implementation, and implements a caching procedure employed in the partial forward model evaluations within a Markov chain Monte Carlo framework.